A391672 - OEIS

%I #18 Dec 22 2025 17:37:31

%S 1,9,6,1,5,7,0,5,6,0,8,0,6,4,6,0,8,9,8,2,5,2,3,6,4,4,7,2,2,6,8,4,7,8,

%T 0,7,3,9,4,7,8,6,7,4,6,1,7,8,6,6,7,2,1,9,0,0,0,5,8,3,2,1,7,7,0,9,0,6,

%U 1,3,0,2,7,0,9,9,2,1,0,1,2,7,8,3,0,1,2,9

%N Decimal expansion of sqrt(2+sqrt(2+sqrt(2))).

%C Algebraic integer of degree 8.

%C Largest positive real root of x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 2 = 0. The eight roots are s2*sqrt(2+s1*sqrt(2+s0*sqrt(2))), where s2, s1, s0 in {-1, 1} (see also A391673, A391674 and A272535).

%H Wolfdieter Lang, <a href="/A187360/a187360.pdf">Minimal Polynomials of 2*cos(Pi/n)</a>

%H <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>

%F Equals 2*cos(Pi/16) = 2*A232737.

%e 1.96157056080646089825236447226847807394786746178667...

%t RealDigits[Sqrt[2+Sqrt[2+Sqrt[2]]],10,88][[1]] (* _Stefano Spezia_, Dec 17 2025 *)

%Y Cf. A187360, A272535, A391673, A391674.

%K nonn,cons,easy

%O 1,2

%A _A.H.M. Smeets_, Dec 16 2025